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MYU Tokyo
S & M 3377

Experimental Analyses of Aerodynamic Force Generationand Wing Motion Associated with a Single-motor-driven
Butterfly-inspired Flapping-wing Robot
Shogo Miyasaka,1 Chang-kwon Kang,2 and Hikaru Aono1*
1Shinshu University, 3-15-1, Tokida, Ueda 386-8567, Japan

2The University of Alabama in Huntsville, Huntsville, Alabama 35899, U.S.A.

(Received February 3, 2023; accepted March 7, 2023)

Keywords: flapping wing, butterfly-inspired aerial robot, simultaneous measurement, elastic band, single
motor

The fascinating flight traits of butterflies, such as low wing loading, low flapping frequency,
and the ability for long-distance flight, have intrigued scientists and engineers. To study thesemechanisms, a 2.7 g butterfly-inspired flapping-wing micro air vehicle (FWMAV) was
developed using a combination of a single motor, elastic bands, a driving shaft, shape
optimization, and a butterfly-like wing planform. During tethered experiments, aerodynamic
forces and wing motions were simultaneously measured to understand the aerodynamics of thebutterfly-inspired FWMAV. The results show that the ranges of resultant flapping and lead-lag
motion of the wing of the robot were within those of real butterflies during the first stroke. The
lift varied with the flapping motion and was sufficient for flight but averaged to zero over one
flapping cycle because the opposite direction of lift was generated during the upstroke. Thesefindings indicate that the modulation of the resulting aerodynamic force direction due to thecontrol of the stroke plane angle per stroke plays a crucial role in the flights of butterflies andbutterfly-inspired FWMAVs.

1.

Introduction

The functions of animals have been a topic of interest for many scientists, and thedevelopment of bio-inspired robots has been on ongoing field of study for a long time.(1–3)
Flapping-wing micro air vehicles (FWMAVs)(4,5) were inspired by the movements and functionsof the wings and bodies of flying insects and birds.(6,7) It is expected that FWMAVs will be used
as an element of observation and information gathering systems for unknown and hazardous
environments. Owing to advances in manufacturing technology and a better understanding offundamental aerodynamic mechanisms in flapping wing aerodynamics, several types of bioinspired FWMAVs have demonstrated controlled f light in indoor (8,9) and outdoor
environments.(10–14)*Corresponding author: e-mail: aono@shinshu-u.ac.jp

https://doi.org/10.18494/SAM4343

ISSN 0914-4935 © MYU K.K.
https://myukk.org/

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Among many biological flyers, we focus on the flights of butterflies and a butterfly-inspired
FWMAV in this study. One of the motivations comes from the observations that species ofbutterflies (e.g., chestnut tiger and monarch butterfly) migrate over long distances acrosscontinents(15,16) and fly at high altitudes.(17) Furthermore, the flights of butterflies arecharacterized by a low wing loading and a low flapping frequency in comparison with those ofother insects. Moreover, butterflies use the change in stroke plane angle between the downstroke
and the upstroke to modulate the direction of aerodynamic forces and torques, whereas mostflying insects and birds change the direction of lift force by changing the pitching angle of theirwings.
Fujikawa et al. built a 1 g butterfly-style flapping robot based on a rubber-band-driven crankmechanism.(18) Using this robot, they looked at the effects of the relative position of the center oflift on the resulting flight behavior.(18) Subsequently, a simple slide-crank mechanism
incorporating flexible links was added to the robot to achieve both flapping and lead-lag
motions,(19) and the glide characteristics and attitude stability of the modified robot were
investigated.(20) At the same time, Tanaka and Shimoyama built a 0.39 g butterfly-type
ornithopter based on the rubber-band-driven crank mechanism.(21) They investigated an inactivefeathering or feedback control of the wing motion that would be a possible mechanism behindthe stable forward flight of swallowtail butterflies.(21) Rubber actuator models are simple
structures and exhibited a high power/mass ratio even though the flight distance is very shortbecause the actuator only flaps the wings a couple of times because the twisting torque quickly
decays.
To increase the flight distance and analysis area, Fujikawa and Kikuchi developed a 0.9 g
butterfly-style flapping wing robot without a battery based on a single motor and elastic
bands.(22) A posture control mechanism of the robot was tested by varying the ratio ofdownstroke and upstroke times,(22) and the effects of flapping motion on gliding performance
were measured.(23) There were also 55 g butterfly-like flapping robots with tenfold enlarged
wings,(8) which were able to fly. However, the wing motion and the trajectory of the center ofgravity of the robots were different from those of actual butterflies. The main reason was thatthe movements of the wings and bodies of butterflies were more challenging to reproduce using
mechanical parts than those of other insects owing to the considerable interaction between thewing and the body.(24,25)
Previous studies(8,14,18–25) have shown progress in developing butterfly-inspired FWMAVs
and understanding butterfly flight mechanisms, but the connection between aerodynamic force
and wing and body motions in robots remains unclear. In this study, we aim to shed light on theissue by constructing a single-motor-driven butterfly-inspired FWMAV and investigating therelationship between wing motion and aerodynamic force generation through simultaneous
measurements under tethered conditions. The aerodynamic forces produced by the FWMAV are
tracked using a force transducer, and wing motion is captured in real time by two high-speed
cameras.

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2.

Materials and Methods

2.1

Butterfly-inspired flapping wing robot design

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Figure 1 illustrates the design of the butterfly-inspired FWMAV, named robo-butterfly
Shinshu, with a bird’s eye view of the structure and mechanism of its wing actuation, and adetailed view of the separated components of the wing planform. The robo-butterfly Shinshu
has a wingtip-to-wingtip length of 175 mm, a forewing span of 80 mm, and a hindwing span of
43 mm, similar to previous studies.(18,19,22,23) Its wing is made of a 12.5 μm Kapton film
reinforced with 0.3 mm carbon rods serving as veins. The design of the wings was based on the
dynamic similarity(6) by matching the Reynolds numbers, reduced frequency, and angle ofattack. In addition, the aspect ratio, wing loading, and flapping frequency were chosen so thatthese were close to the range of real butterflies.(26,27) Moreover, the effects of the vein structuresof the real butterfly wings were not considered and are one of our on-going research topics.(28,29)
The body frame is constructed using an acrylic resin (AR-M2), designed with CAD software(Fusion360, Autodesk), and fabricated using a 3D printer (AGILISTA-3200, Keyence). The
motor box geometry was optimized to reduce weight. The robot weighs 2.70 g (W = 0.026 N),
including a pinion gear (GW338, DIDEL), a spur gear (G336L, DIDEL), a motor (MK04-10,
DIDEL), and a Li-Po battery (FX10S, 10 mAh, 15C/150 mA), and has a wing loading of 3.63 N/
m2 with a total wing area of 7312 mm2, comparable to that of real butterflies.(16–19,26,27) Figure 2
shows the mass distribution of the robo-butterfly Shinshu. Figure 1(b) shows the motion of theFig. 1. (Color online) (a) Overview of the robo-butterfly Shinshu, a butterfly-inspired FWMAV. (b) Magnified
view of the wing actuation mechanism. (c) Exploded view of the main structures of the robo-butterfly Shinshu andwing planform of fore- and hindwings.

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Fig. 2.

(Color online) Mass breakdown of the robo-butterfly Shinshu.

motor being converted to a reciprocal flapping motion through a crank mechanism. The wingalso undergoes a lead-lag motion through an elastic band connected to the drive shaft, similar toprevious studies.(19,21) The elastic band is made of a 125-μm-thick Kapton film and is 4 mm wideand 33 mm long. Its shape and attachment were determined through trial and error. The robobutterfly Shinshu’s design emphasizes a flapping motion with a lead lag, a forward center of lift,
and a large flapping amplitude, based on the observations of real butterflies(19) and previous
studies using the robot.(21,22) The motor and gear unit are located at the rear of the body to place
the center of gravity near the rear. The pitch motion of the body is not included in the design ofthe model presented in this study.
The referenced flapping and lead-lag angle histories of a real butterfly were those of aswallowtail butterfly (Paplio xuthus) during the first stroke reported in a previous study.(19) The
range of the flapping angle was from −60 to 80° and the range of the lead-lag angle was from −5
to 15°. The frequency of the lead-lag angle was twice the flapping frequency.
2.2

Measurement of aerodynamic force and wing motion

Figure 3 shows that the experimental setup used to investigate the relationship between thewing motion and aerodynamic force generation of the robo-butterfly Shinshu involved the use ofa six-axis force transducer (ATI Nano17 Ti, ATI Industrial Automation), a data acquisition
device (USB-6341, National Instruments), a PC, and two high-speed cameras (HAS-DX, Ditect).
The force transducer was used to measure aerodynamic force and torque and was connected to acomputer with a sampling frequency of 2000 Hz. The wing motion was recorded using the twohigh-speed cameras with a sampling rate of 2000 frames per second, and a light source (PFBR150SW-MN, CCS) was used to improve the quality of the recorded video. The eight markers on
the right wing were tracked and analyzed using an in-house photogrammetric deformation
measurement program,(30) and the 3D coordinates of all markers were recorded and analyzed.
An external power supply (PW8-3AQP, Texio) provided stable electrical power to the robo-

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Fig. 3. (Color online) (a) Experimental setup of the simultaneous lift and wing motion measurement, (b) magnified
view of the robot, and (c) tracking markers on the fore- and hindwings.

butterfly Shinshu with a voltage of 4.2 V and a current of 0.15 A. This input condition is thesame as that of a Li-Po battery that will be installed. A low-pass filter with a cutoff frequency offour times the flapping frequency was applied. Thrust (Fx) and lift (Fz) were defined as theforces in the x- and z-axis directions, respectively, in the coordinate system.
Figure 4 shows the wing coordinate system used to analyze the wing motion of the robobutterfly Shinshu. The lead-lag angle (θ) and flapping angle (ϕ) are defined in Fig. 4. The stroke
plane is along the z w -axis. Flapping frequency was computed by the frequency analysis of thetime history of the flapping angle. The data was recorded for 0.5845 s, which included three
flapping cycles. Cycle-averaged data were computed on the basis of three flapping motions(denoted by an upper bar symbol). The cycle-averaged lift and thrust are discussed on the basisof this information.

3.

Results and Discussion

Figure 5 shows the time histories of aerodynamic forces and wing angles at the tip of theforewing [i.e., pt #4 in Fig. 3(c)]. The flapping frequency was 7.0 Hz and the period of flapping
motion (T) was 0.1429 s. Results from the switching on the robo-butterfly Shinshu (t/T = 0) toaround t/T = 0.9 are not considered in the discussion.

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Fig. 4. (Color online) (a) Schematic diagrams of wing coordinate system and (b) definitions of flapping angle andlead-lag angle θ.

Fig. 5. (Color online) Time histories of aerodynamic forces (Fx and Fz) and wing angles at the wing tip (ϕ and θ). T,
D.S., and U.S. denote the period of flapping motion, downstroke, and upstroke, respectively.

The lift (Fz) and thrust (Fx) change as the wing angles change. During the downstroke,positive lift is generated, whereas negative lift is produced during the upstroke. The half stroke
average data shown in Table 1 indicates that the lift generated during the downstroke is sufficient
to offset the weight of the robo-butterfly Shinshu. Although the half stroke average lift isnegative, its magnitude is larger than the weight of the robo-butterfly Shinshu. The lift has two
peaks, with the first and largest peak appearing in the early downstroke, and the second near theend of the downstroke. Negative thrust is generated during most of the stroke, and both cycle andhalf stroke average thrusts are negative, implying that drag is generated. The magnitude of lift ismuch larger than that of thrust owing to the appearance of a large angle of attack of the wing
during both strokes (the average values are approximately 98 and 80° over the downstroke andupstroke, respectively).
Figure 6 shows a comparison of the time histories of the flapping and lead-lag angles of thewing between the robo-butterfly Shinshu and a real butterfly in the first stroke.(19) The ratio ofthe downstroke and upstroke was around 60:40. The ranges of the flapping and lead-lag angles

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Table 1
Averaged aerodynamic force data and ratio of aerodynamic force and weight. W denotes the weight of the robobutterfly Shinshu.
Cycle average
Downstroke average
Upstroke averageFx| Fx / W |Fz| Fz / W |−0.013 N−0.008 N−0.005 N

0.49

0.30

0.19

0.007 N

0.041 N

−0.034 N

0.26

1.55

1.28

Fig. 6. Comparison of time histories of (a) flapping angle (ϕ) and (b) lead-lag angle (θ) of the forewing between therobo-butterfly Shinshu and a real butterfly.(19) T denotes the period of flapping motion.

of the robo-butterfly Shinshu are comparable to those of a real butterfly.(19) The time histories ofthe flapping angle of the robo-butterfly Shinshu are in close agreement with the data of realbutterflies. However, further improvement of the time histories of the lead-lag angle of the robobutterfly Shinshu is required. The lead-lag angle is almost constant during the downstroke but
decreases during the upstroke. Furthermore, the rates of changes in flapping and lead-lag angle
also change as seen in Figs. 5 and 6. The rate of change in flapping angle changes at the end of
the downstroke, whereas the rate of change in lead-lag angle changes at the stroke reversal from

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the upstroke to the downstroke. This is likely due to the stretch and twist of the elastic band
attached to the driving shift. The Reynolds number, reduced frequency, and aspect ratio of therobo-butterfly Shinshu were 5738, 0.43, and 4.19, respectively, which are within the range of realbutterflies.(17,19,26,27) The angle of attack for the robo-butterfly Shinshu is purely due to the wing
deformation (i.e., passive pitch). When the resulting angle of attack is close to the butterfly
motion, dynamic similarity(6) is achieved such that the flow structures around the wings are
similar to those reported in previous studies.(26,27)
Figure 7 shows the time histories of the flapping and lead-lag angles reconstructed from thepositions of markers on the fore- and hindwings shown in Fig. 3(c) (see the supplementary
video). The time histories of flapping angles of all points indicated that the fore- and hindwings
flapped with insignificant bending deformation. Also, the time-varying lead-lag angle of all
points indicated that the motion of the forewing resembled a rigid rotation without notable
deformations. Results implicate that the wings of the robo-butterfly Shinshu acted as a very thin
rigid-like flat plate.

Fig. 7. (Color online) Time histories of (a) flapping angle (ϕ) of fore- and hindwings and (b) lead-lag angle (θ) of
the forewing. T and D.S. denote the period of flapping motion and downstroke, respectively.

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Fig. 8. (Color online) (a) Time histories of flapping angle and local sectional angle of attack of forewing and (b-1,b-2) schematic diagrams of resulting aerodynamic force acting on the wing and the angle of attack over the stroke.
(b-3) Illustration of effects of stroke plane angle modulation on the resultant aerodynamic force acting on the wing
during the upstroke.

On the basis of the 3D coordinate data of two points of the forewing (i.e., pt #1 and #4), thelocal sectional angle of attack (AoA) was calculated. Figure 8 shows the time histories of thelocal sectional AoA and flapping angle of the forewing and illustrates a schematic diagram of
the resulting aerodynamic force acting on the wing section. Looking at Figs. 5 and 8, themaximum positive lift generation occurred when the local sectional AoA of the forewing wasclose to 90°. The AoA of the forewing remained constant in most of the strokes. The large local
sectional AoA implies flow separation from the leading and trailing edges. As such, it is likelythat the leading and trailing-edge vortices during both strokes are generated, resulting in theinsect unsteady flow mechanisms. As explained in Fig. 8(b), the modulation of lift force during
the upstroke appeared promising for less negative lift generation in one flapping cycle and the
reproduction of butterfly-like body motion due to the change in the direction of the resulting
aerodynamic forces acting on the wing.

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Conclusions

In this study, we developed a 2.7 g butterfly-inspired FWMAV with an on-board battery,
named the robo-butterfly Shinshu. The flapping and lead-lag motions of the wings weregenerated using an elastic band, a single motor, a driving shaft, and flapping/lead-lag joints. The
results of the simultaneous measurements of wing motion and aerodynamic forces under thetethered condition showed that the robo-butterfly Shinshu flapped at a rate of 7.0 Hz, generated
lift during the downstroke, which is large enough to offset its own weight, and had a cycleaveraged lift close to zero. Results suggest the importance of the modulation of the stroke planeangle to adjust the direction of the resulting aerodynamic force generated by the wings during
the flight of butterflies and butterfly-inspired FWMAVs. The current experiments of thetethered robo-butterfly Shinshu did not include the body pitching motion. Future work will
focus on developing a rotation mechanism of the stroke plane for the robo-butterfly Shinshu todemonstrate stable forward flight and reproduce the movements observed in real butterflies.

Acknowledgments
This work was partly supported by the Japan Society for the Promotion of Science
KAKENHI Grant Number JP22H01397. CK was partly supported by the National Science
Foundation (grant number CMMI-1761618). The authors thank Dr. Taku Nonomura, Dr. Keisuke
Asai, Dr. Yuta Ozawa, and Mr. Kento Akama for their support in the measurement of wing
deformation.

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About the Authors
Shogo Miyasaka received his B.S. degree from Shinshu University, Japan, in
2021. Since 2021, he has been a graduate student at the Department of
Biomedical Engineering, Graduate School of Science and Technology,
Shinshu University. His research interests are in butterfly flight and bioinspired aerial robots. (21bs219e@shinshu-u.ac.jp)

Chang-kwon Kang received his B.S. and M.Sc. degrees from Delft Universityof Technology, Netherlands, in 2001 and 2005, respectively, and his Ph.D.
degree from the University of Michigan, Ann Arbor, MI. From 2011 to 2013,
he was a postdoctoral research fellow at the University of Michigan, Ann
Arbor, MI. From 2013 to 2019, he was an assistant professor at the Universityof Alabama in Huntsville, AL. Since 2019, he has been an associate professor
at the University of Alabama in Huntsville, AL. His research interests are in
unsteady aerodynamics, bioinspired aerospace engineering, computational
fluid dynamics, and fluid-structure interaction. (ck0025@uah.edu)

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Hikaru Aono received his B.S., M.S. and Ph.D. degrees from Chiba
University, Japan, in 2004, 2005, and 2008, respectively. From 2008 to 2011,
he was a postdoctoral research fellow at the University of Michigan, Ann
Arbor, MI. From 2011 to 2015, he was a research scientist at the Japan
Aerospace Exploration Agency. From 2015 to 2020, he was an assistantprofessor at Tokyo University of Science, Japan. Since 2020, he has been an
associate professor at Shinshu University. His research interests are inflapping-wing aerodynamics and robots, computational fluid dynamics, flight
dynamics and control, and flow control. (aono@shinshu-u.ac.jp)